With stretched ears, the possibilities of jewelry are almost infinite. All of those things can get confusing once you're looking at the website with a million different options. One of the options on a lot of plugs are no flares, flares (on one side), or double flares.
No flare means that the plug is just even the entire way. It's a 0 gauge all the way across. A lot of these plugs will come with screw on backs or o-rings so that they don't fall out or you may for example have a silicone pair that has edges on it. These are still no flare, as they're the same size all the way across. Here is a pair that we have on our website, http://www.eargauges.net/stainless-steel-plugs/no-flare-stainless-steel-tunnels.html.
Single Flare means that it's just flared out on one side. These gauges are the same as no flare except that one side (the front) had a lip on it, so to speak, so that the plug doesn't fall out. Single flare plugs normally come with o-rings to put on the backside so that they don't fall out. Have a look at a pair from the shop, http://www.eargauges.net/6g/oline-single-flare-tunnels.html.
Double flare is when both sides flare out. Here's another picture for example, http://www.eargauges.net/stone-plugs/abstraction-stone-plugs.html . This keeps the plug from falling out and it looks nice. The ends are a little bit bigger than the plug so that they don't fall out.
Your preference on size, material, and flares all makes your stretching unique.